Aircraft: COMMERCIAL FIXED WING
Phase of flight: Taxi
Anomaly: Deviation / Discrepancy - Procedural Clearance; Ground Event / Encounter FOD; Ground Excursion Taxiway; Ground Incursion Taxiway

I; the First Officer; executed the charted Visual Approach. Landing was uneventful and rolled to taxiway Tango before passing controls to the Captain to taxi to gate. As we exited the runway Tower gave taxi instructions to the gate. and to '... stay with me'. I read back the taxi instructions and the Captain repeated them as he commenced taxi from the runway and stated 'flaps up'. I then commenced my after landing flow; raised the flaps; checked speed brakes stowed; autobrakes off; flight directors off; wing lights off; steady and strobe to steady; trimmed to 5 units; check weather radar off; cycled ramp (though not needed) to active in VHF2; and started removing flight pertinent printer strips. By this time we were somewhere near the Bravo; Golf; Sierra taxiway junction. I briefly looked up as Captain stated; 'There's Golf'. I don't remember what I heard exactly that caused me to look up again; some reference to Golf taxiway perhaps. But when I looked up I did not recognize where we were. I saw lighted taxi signs for Sierra; Golf; and Bravo in the distance to the left. I could see blue taxiway edge lights all around but nothing in front of us. The blue taxi edge lights were very disorienting especially without a lit taxi center line. Our taxi and turnoff lights were so dim that they were essentially useless. The moon was providing more light than they were. On my IPAD I could see our own ship; we were on Golf but heading the wrong way. The Captain had turned right instead of left. At that point he turned left in an attempt to get back to Alpha taxiway; I assume. He did make me aware that he was concerned about accidentally crossing on to the runway. Due to the very poor lighting and the sea of blue taxi edge lights; taxiway was difficult to discern from anything else. All you could see was directional taxi signs in the darkness and blue taxi lights scattered about. The Captain turned left until there was a break in the blue lights with the Bravo sign visible just a little further away so it did appear as though we were turning on taxiway Bravo though I could see no yellow line. I told him I didn't see the taxiway; I think we're going in to no man's land; and Captain said; no; we're on Golf; there's the sign for Bravo. I was confused about the blue lights; they didn't seem to be oriented right and the our ship was sort of on Golf but pivoting so I allowed the events to progress thinking maybe I was just disoriented. When we proceeded ahead the ground before us was just dark. Really no discernible features except for blue taxi lights up ahead that seemed to mark the edge of Bravo. I said I think we're off the taxiway. Captain stopped. We exchanged thoughts on the best way to proceed from that point. We called tower to confess. Tower took a look; said we were just near Bravo; or Golf; I can't remember exactly but he was not concerned which taxiway we ended up needing to get to the gate. I thought we might not be on prepared surface but the Captain was sure we were still on the taxiway just facing the wrong direction. So I told him clear to the right; let's turn all the way back around and take Bravo. The Captain turned tight right and proceeded back the way we came. The jet stopped and thinking it was an incline the Captain added power and we rolled back on taxiway center; turned left on Bravo; took Foxtrot then Alpha to the gate; tower then stated; 'Not a problem guys; the snow plows do more damage than you'. No other occurrences from then on. We did discuss the possibility that we may have left the taxiway. The Captain was confident we had not and I was inclined to believe him since I could not see the ground beneath us; we were just avoiding taxi edge lights. I told him I would check and do an external walk around once we shut down. During deplaning maintenance met me before walking out. She asked me if the landing was rough and I said; actually; no; the landing was great... WHY? She showed me a shot on her cell phone of our nose strut and this is your nose gear. It was covered with dirt. I went down to look at it and it was dirty but both tires were still intact at that point and I saw no evidence of anything else on the mains or the engines. The mains were spotless; engines were clean. I came back up; told the Captain the mains were covered in dirt on the tires and on the lowermost part of the strut. I then stepped out of the cockpit while he talked to maintenance. We turned the plane over to maintenance; they said they would check out the gear and clean it off and we left; still not sure we actually left the taxiway. The wind was blowing in excess of 30 knots and dirt was blowing all over. We chalked it up to that.It was dark; really dark on that end of the airport. The taxiways are a conglomeration that looks more like spaghetti. The whole area is labeled HS1; for good reason. They are difficult enough to navigate in daylight; much less at night with no centerline lighting; a plethora of edge lights all outlining various 'islands' on the field; taxiway ID and directional signs for every taxiway that intersects in HS1 and a useless taxi light. That is a lot of scattered lights with no reliable taxi light to help gauge distance. The Captain was disoriented. Golf taxiway is constructed right on the curve at a 45 degree angle. The directional sign at night can make the left turn on Golf easy to miss especially with the opposite direction of Golf being directly in front of you. I; the First Officer was task distracted. I was performing after landing flow and cockpit cleanup. The Captain had told me during this trip that he was once based in [the area] and was very familiar with this airport; not to mention he was a check airman. My guard was down and I was not as diligent as I normally am during the taxi operation. Being tired and expectation bias. It was night; the end of the day in serious winds. The Captain and I were exhausted most of our mental energy on planning the approach and landing given the conditions that night. The approach was not exactly a standard one we do all the time; and we were not landing on the usual runway you get at this airport. A better taxi light would have alleviated much of the confusion. The lights are not adequate. Neither of us was really sure that we ever left the taxiway. Taxiway centerline lights. There are many islands outlined in blue and no green center lights to actually show the trail through the maze of them. Distance judging is difficult in the dark and it was dark for us. Those lights would have helped. I should have stayed more engaged in the taxi phase to back up my Captain. Getting lost is going to happen and there are two of us for a reason. I allowed myself to get disoriented as well. Landed Runway 31 LGA. Cleared at taxiway T. ATC gave us T;B;G;A to gate. Turned right on Taxiway G instead of left. Area was extremely dark; appeared to taxi over some Foreign Object and Debris (FOD) on taxiway G. After arriving at gate was informed one nose tire was flat. The area around taxiway G is confusing; especially at night. The area is not marked well and very dark making it extremely hard to find correct taxiway. Light up the area better. Better taxiway designations. Area should be redesigned. Air carrier flight crew reported turning the wrong way on a taxiway at night and when turning around exited the taxiway surface due to poor taxiway lighting and markings at LGA airport.